Turning without going anywhere
Here is what is curious about a couple: it turns a body, and yet it takes that body nowhere at all.
The resultant is zero
From chapter 9 we know that the resultant of two forces acting in opposite directions along one line is the difference between them. In a couple the two forces are equal in magnitude, so that difference is zero.
resultant = F − F = 0
If the resultant force is zero there is no unbalanced force on the body. So a couple does not move a body linearly.
And yet it turns
The two moments do not cancel in the same way. Because the forces act along two different lines, both of them turn the body the same way round. So the moments add.
Opposite, so they cancel → no linear motion
Same way round, so they add → there is rotation
The body turns about a point lying between the two forces. If it is not pivoted, that point is at the centre of the body itself.
Adding forces is not adding moments
That two forces add to zero does not mean their moments add to zero. A couple is the clearest example there is that the two are separate questions.